Resumo de Equações - Circuitos

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EE2111 Useful Equations
Current and Charge
 
Power and Energy
 
Resistors 
 ; 
Resistors in Series: 
Resistors in Parallel: 
Two Resisrors in Parallel: 
 Transformation
 ; .....
Voltage Divider: ; ...
Current Divider: ; ...
Operational Amplifiers
Inverting Op-Amp: 
Non-Inverting Op-Amp: 
Weighted Inverting Summer: 
 
Inductors
; ; 
Inductors in Series: 
Inductors in Parallel: 
Capacitors
; 
Capacitors in Series: 
Capacitors in Parallel: 
RL Circuit (Natural Response)
 ; t > t0 
RL Circuit (Step Response)
 ; t > t0 
RC Circuit (Natural Response)
 ; t > t0 
RC Circuit (Step Response)
 ; t > t0 
RLC Circuit (Natural Response)
; ; 
 
Overdamped: 
 
Underdamped:
 
 ; 
Critically damped: 
 
i td
dq= q t  i td
t0
t
 q t0 +=
p td
dw= w t  p td
t0
t
 w t0 +=
v iR= p i2R v
2
R
-----= =
Req R1 R2 + +=
1
Req
--------- 1
R1
------ 1
R2
------ .....+ +=
Req
R1R2
R1 R2+
--------------------=
 Y
Z1
ZbZc
Za Zb Zc+ +
----------------------------------=
v1 Vs
R1
R1 R2+
--------------------  
 
=
i1 Is
R2
R1 R2+
--------------------  
 
=
G
R2
R1
------–=
G 1
R2
R1
------+=
v0
Rf
R1
------v1
Rf
R2
------v2 
Rf
Rn
------vn+ + +  
 
–=
v L td
di= i t  1L--- v td
t0
t
 i t0 += WL 12---Li2=
Leq L1 L2 + +=
1
Leq
-------- 1
L1
------ 1
L2
------ + +=
i C td
dv= v t  1C---- i td
t0
t
 v t0 += WC 12---Cv2=
1
Ceq
--------- 1
C1
------ 1
C2
------ + +=
Ceq C1 C2 + +=
i t  I0e
t t0–
------------- 
 –
=  LR---=
i t  If I0 If– e
t t0–
------------- 
 –
+=
v t  V0e
t t0–
------------- 
 –
=  RC=
v t  Vf V0 Vf– e
t t0–
------------- 
 –
+=
Parallel 12RC-----------= Series
R
2L
------= 0 1LC------------=
s1 2 – 2 02–=
f t  A1es1 t A2es2 t+=
td
df 0  s1A1 s2A2+=
f t  e  t– B1 dt cos B2 dt sin+ =
td
df 0  dB2 B1–= d 02 2–=
f t  e  t– D1 t D2+ =
td
df 0  D1 D2–=
EE2111 Useful Equations
Phasor Domain
 ; V = 
 ; I = ; 
 ; ; 
Sinusoidal Power Calculations
Instantaneous Power: 
 
Effective or rms value:
 
Average Power:
 
Reactive Power:
 ; 
Complex Power: 
 
For Impedance Load: ; 
 
 ; 
v t  Vm  t v+ cos= Vm v
i t  Im  t i+ cos= Im i
R R L jL C jC--------–
p P P 2 t cos Q 2 t sin–+=
Feff = Frms
1
T
--- f t  2dt
t0
t0 T+
=
P
VmIm
2
-------------- v i– cos VeffIeff v i– cos= =
Q
VmIm
2
-------------- v i– sin VeffIeff v i– sin= =
pf v i– cos= rf v i– sin=
S P jQ+ 12
---VI* VeffIeff
*= = =
Z R jX+= Veff ZIeff=
S Ieff
2Z
Veff
2
Z---------------- P jQ+= = =
P Ieff
2R= Q Ieff
2X=